# 12.9: What’s the Difference Between McNemar and Independence?

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Let’s go all the way back to the beginning of the chapter, and look at the `cards`

data set again. If you recall, the actual experimental design that I described involved people making * two* choices. Because we have information about the first choice and the second choice that everyone made, we can construct the following contingency table that cross-tabulates the first choice against the second choice.

`cardChoices <- `**xtabs**( ~ choice_1 + choice_2, data = cards )
cardChoices

```
## choice_2
## choice_1 clubs diamonds hearts spades
## clubs 10 9 10 6
## diamonds 20 4 13 14
## hearts 20 18 3 23
## spades 18 13 15 4
```

Suppose I wanted to know whether the choice you make the second time is dependent on the choice you made the first time. This is where a test of independence is useful, and what we’re trying to do is see if there’s some relationship between the rows and columns of this table. Here’s the result:

**chisq.test**( cardChoices )

Alternatively, suppose I wanted to know if * on average*, the frequencies of suit choices were different the second time than the first time. In that situation, what I’m really trying to see if the row totals in

`cardChoices`

(i.e., the frequencies for `choice_1`

) are different from the column totals (i.e., the frequencies for `choice_2`

). That’s when you use the McNemar test:**mcnemar.test**( cardChoices )

```
##
## McNemar's Chi-squared test
##
## data: cardChoices
## McNemar's chi-squared = 16.033, df = 6, p-value = 0.01358
```

Notice that the results are different! These aren’t the same test.